Factor –7x3 + 21x2 + 3x – 9 by grouping. what is the resulting expression? (3 – 7x)(x2 – 3) (7x – 3)(3 + x2) (3 – 7x2)(x – 3) (7x2 – 3)(3 + x)

Using the reverse-FOIL method, we begin by noting that the resulting terms are going to be:

(7x^2 and 3) on the first term, and (x and 3) on the second term. The goal is to find where the positive and negative signs are placed to get the proper final quadratic result. In this case, by looking at the final term, (-9), we know that the 3s will be one positive and one negative. Also, we know that, with the 3rd term, (3x), we realize that the 2nd term and 3rd terms have to be either both positive or both negative. However, we also find that the first result, (-7x^3), means that the 3rd term must be a positive.

This gives us a (-7x^2 + 3) for the first term and (x - 3) for the second term:

(-7x^2 + 3) (x - 3) multiplies out to (-7x^3 + 21x^2 + 3x - 9).